Phaseless Antenna Characterization by Effective Aperture Field and Data Representations
TL;DR: An extensive numerical and experimental analysis endorses the algorithm reliability and accuracy and confirms its usefulness for antennas having a general radiating (vector) behavior, i.e., either focusing or non-focusing.
Abstract: The problem of antenna characterization from phaseless near-field data is addressed by appropriate use of the available information on the Antenna Under Test (AUT) and on the scanning geometry to provide efficient representations for both the unknowns and the data. Such a strategy allows improving the reliability and the accuracy of the proposed characterization algorithm and, at the same time, shortens the overall measurement process. An extensive numerical and experimental analysis, together with a comparison with existing approaches, endorses the algorithm reliability and accuracy and confirms its usefulness for antennas having a general radiating (vector) behavior, i.e., either focusing or non-focusing.
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TL;DR: An overview of the application of the band-limitation properties and non-redundant sampling representations of electromagnetic fields to NF-FF transformations is presented in this paper, where the progresses achieved by applying them to data acquired on conventional NF scanning surfaces are discussed, outlining the remarkable reduction in the number of needed NF samples and measurement time.
Abstract: An overview of the application of the band-limitation properties and nonredundant sampling representations of electromagnetic fields to NF-FF transformations is presented. The progresses achieved by applying them to data acquired on conventional NF scanning surfaces are discussed, outlining the remarkable reduction in the number of needed NF samples and measurement time. An optimal sampling interpolation expansion for reconstructing the probe response on a rotational scanning surface from a non-redundant number of its samples is also discussed. A unified theory of the NF-FF transformations with spiral scannings, which allow a remarkable reduction of the measurement time, is then reviewed by describing a sampling representation of the voltage on a quite arbitrary rotational surface from its nonredundant samples collected on a proper spiral wrapping it. Some numerical and experimental results assessing the effectiveness of the considered NF-FF transformations are shown too.
90 citations
TL;DR: In this article, the authors address the problem of extracting the maximum amount of information on an electromagnetic field over a domain DO from field sample measurements on a domain DI, with a priori information on the source (or scatterer).
Abstract: [1] We address the problem of extracting the maximum amount of information on an electromagnetic field over a domain DO from field sample measurements on a domain DI, with a priori information on the source (or scatterer). The problem is faced in two steps. In the first one, the source reconstruction is dealt with by taking into account the available a priori information and the optimal probe positioning is determined as that optimizing the singular value dynamics of the involved linear radiation operator. The second step consists of reconstructing the field on DO as that radiated by the retrieved source. An extensive numerical analysis highlights the performance of the approach.
49 citations
TL;DR: In contrast to other off-axis schemes, the proposed system does not require neither mechanical nor electrical phase shifting and, therefore, it can be directly adapted to a large number of frequency bands.
Abstract: This paper presents a broadband and phaseless synthetic aperture radar (SAR) with efficient sampling. The design relies on a novel phaseless monostatic element comprising a transmitter and a receiver. This element, together with a computationally inexpensive algorithm, can retrieve the phase of the monostatic scattered field at all the working band except for two small safety margins at the lower and upper frequencies. Furthermore, the phase retrieval works independently of the transmitter/receiver position. Consequently, conventional approaches to reduce the number of monostatic acquisition points can be employed. Thus, the proposed strategy is suitable to implement either arrays that benefit from a reduced number of low-complexity elements or raster scan systems that benefit not only from the cost reduction of the scanning components but also from a remarkable speed-up due to the reduced number of acquisition points. Moreover, in contrast to other off-axis schemes, the proposed system does not require neither mechanical nor electrical phase shifting and, therefore, it can be directly adapted to a large number of frequency bands. The performance of the system is validated by simulation and measurement examples in the millimeter-wave band.
43 citations
Cites background from "Phaseless Antenna Characterization ..."
...The signal corresponding to the square amplitude of an electromagnetic field has a spatial bandwidth, which is twice the spatial bandwidth of a conventional acquisition [44], [14]....
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...Moreover, the approach has been reported to be compatible with schemes to reduce the number of acquisition points [14]....
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TL;DR: This work presents a POS, power pattern synthesis technique of conformal, shaped-beam reflectarrays, based on the p-series approach, on non-uniform FFTs, and on fast implementations of the FFT and of matrix–vector and vector–vector multiplications.
Abstract: Phase-only synthesis (POS) techniques represent an important tool for reflectarray design. Indeed, although based on approximate scattering models, for planar antennas, they are numerically effective thanks to the use of fast Fourier transform (FFT) routines. Conformal reflectarrays are becoming of interest as they reduce the frequency dependence of the feed/elements path length. Although synthesis algorithms can be extended from planar to conformal geometries, improving computational efficiency is not trivial. We present a POS, power pattern synthesis technique of conformal, shaped-beam reflectarrays, based on the p-series approach, on non-uniform FFTs, and on fast implementations of the FFT and of matrix–vector and vector–vector multiplications. The approach allows modulating computational burden and accuracy, depending on the needs. The method faces crucial issues concerning the reliability of the solution, by adopting a multi-step strategy. At first, the unknown phase shifts are represented by few degrees of freedom and an efficient and effective global optimisation algorithm is applied. Then, assuming as a starting point the obtained solution, all the reflectarray degrees of freedom are taken into account. The computational performance of the approach and its capability in synthesising shaped-beam patterns are discussed against parabolic and faceted reflectarrays, also considering the coverage of an operative mission.
31 citations
30 Sep 2010
TL;DR: Wireless tomography, a novel approach to remote sensing, is proposed in Part I of this series and self-cohering tomography is studied in depth.
Abstract: Wireless tomography, a novel approach to remote sensing, is proposed in Part I of this series. The methodology, literature review, related work, and system engineering are presented. Concrete algorithms and hardware platforms are implemented to demonstrate this concept. Self-cohering tomography is studied in depth. More research will be reported, following this initiative.
30 citations
References
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Book•
21 Dec 2021TL;DR: Part 2 Linear inverse problems: examples of linear inverse problems singular value decomposition (SVD) inversion methods revisited Fourier based methods for specific problems comments and concluding remarks.
Abstract: This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis The authors concentrate on presenting easily implementable and fast solution algorithms With examples and exercises throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems
2,027 citations
"Phaseless Antenna Characterization ..." refers background or methods in this paper
...The purpose of the presented algorithm is therefore to face the inverse problem [8] of reconstructing the s, and thus the aperture field , from the knowledge of the data...
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...and exhibits a step-like behavior of its singular values [29], the ’s can be obtained by means of a singular value decomposition [8] of a properly defined truncated Fourier transform operator....
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...Four main advantages are then obtained: First, the typical ill-conditioning of the near-field phaseless antenna characterization problem [8] is mitigated....
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...A number of algorithms tackling the near-field phaseless antenna characterization, a non-linear inverse and ill-posed problem [8], are now available in the literature [9]–[15]....
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...This further reduces the ill-conditioning [8] and positively affects the reliability of the algorithm [12], [14]....
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TL;DR: In this paper, the authors examined the mathematical truth in the engineering intuition that there are approximately 2WT independent signals ϕ i of bandwidth W concentrated in an interval of length T. Roughly speaking, the result is true for the best choice of the ϕ I (prolate spheroidal wave functions), but not for sampling functions (of the form sin t/t).
Abstract: The purpose of this paper is to examine the mathematical truth in the engineering intuition that there are approximately 2WT independent signals ϕ i of bandwidth W concentrated in an interval of length T. Roughly speaking, the result is true for the best choice of the ϕ i (prolate spheroidal wave functions), but not for sampling functions (of the form sin t/t). Some typical conclusions are: Let f(t), of total energy 1, be band-limited to bandwidth W, and let $\int_{-t/2}^{t/2} \vert f^{2}(t)\vert dt = 1- \epsilon_{T}^{2}$ . Then ${\rm inf}\limits_{\{a_{i}\}} \int_{-\infty}^{\infty} \left\vert f(t)- \sum_{0}^{[2WT]+N]} a_{n}\varphi_{n}\right\vert^{2} dt \lt C_{\epsilon_{T}^{2}}$ is (a) true for all such f with N = 0, C = 12, if the ϕ n are the prolate spheroidal wave functions; (b) false for some such f for any finite constants N and C if the ϕ n are sampling functions.
1,123 citations
"Phaseless Antenna Characterization ..." refers background or methods in this paper
...In particular, the quasi-band-limitedness of both the aperture field and the plane wave spectrum (PWS) along with the mathematical properties of the operator connecting the aperture field to the PWS are exploited to conceive a new strategy, based on a series of prolate spheroidal wave functions (PSWFs) [16], [17], to effectively and efficiently represent the unknown aperture field....
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...ries (7) and (8), only a finite number of terms are needed which is dependent on the values of and and is dictated by the step-like behavior of the eigenvalues corresponding to the 1d-PSWFs [16], [17]....
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...they extend the usual properties of the PSWFs [17], [23]....
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...quasi-optimal expansion can be based on (but not limited to) the use of the rectangular PSWFs (R-PSWFs) [16], [17], [31], that is...
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TL;DR: In this paper, a brief history of near-field antenna measurements with and without probe correction is outlined, beginning with ideal probe scanning on arbitrary surfaces and ending with arbitrary probes scanning on planar, cylindrical, and spherical surfaces.
Abstract: After a brief history of near-field antenna measurements with and without probe correction, the theory of near-field antenna measurements is outlined beginning with ideal probes scanning on arbitrary surfaces and ending with arbitrary probes scanning on planar, cylindrical, and spherical surfaces. Probe correction is introduced for all three measurement geometries as a slight modification to the ideal probe expressions. Sampling theorems are applied to determine the required data-point spacing, and efficient computational methods along with their computer run times are discussed. The major sources of experimental error defining the accuracy of typical planar near-field measurement facilities are reviewed, and present limitations of planar, cylindrical, and spherical near-field scanning are identified.
950 citations
"Phaseless Antenna Characterization ..." refers background in this paper
...thoroughly discussed in [2] and, in [53], it has been underlined that probe compensation is not strictly necessary for electrically small probes....
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TL;DR: Experimental results are given, which indicates that MGS gives $\theta_k$ with equal precision and fewer arithmetic operations than HT, however, HT gives principal vectors, which are orthogonal to working accuracy, which is not in general true for MGS.
Abstract: Assume that two subspaces F and G of unitary space are defined as the ranges (or nullspaces) of given rectangular matrices A and B. Accurate numerical methods are developed for computing the principal angles $\theta_k (F,G)$ and orthogonal sets of principal vectors $u_k\ \epsilon\ F$ and $v_k\ \epsilon\ G$, k = 1,2,..., q = dim(G) $\leq$ dim(F). An important application in statistics is computing the canonical correlations $\sigma_k\ = cos \theta_k$ between two sets of variates. A perturbation analysis shows that the condition number for $\theta_k$ essentially is max($\kappa (A),\kappa (B)$), where $\kappa$ denotes the condition number of a matrix. The algorithms are based on a preliminary QR-factorization of A and B (or $A^H$ and $B^H$), for which either the method of Householder transformations (HT) or the modified Gram-Schmidt method (MGS) is used. Then cos $\theta_k$ and sin $\theta_k$ are computed as the singular values of certain related matrices. Experimental results are given, which indicates that MGS gives $\theta_k$ with equal precision and fewer arithmetic operations than HT. However, HT gives principal vectors, which are orthogonal to working accuracy, which is not in general true for MGS. Finally the case when A and/or B are rank deficient is discussed.
763 citations
"Phaseless Antenna Characterization ..." refers background or methods in this paper
...The values of have been accurately evaluated by the procedure devised in [34]....
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...3), commonly exploited to evaluate the nearness of two subspaces as illustrated in [34], [35]....
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TL;DR: In this paper, a generalization of the generalized prolate spheroidal wave functions is presented, and the eigenvalues of both (i) and (ii) are studied in detail.
Abstract: In two earlier papers∗ in this series, the extent to which a square-integrable function and its Fourier transform can be simultaneously concentrated in their respective domains was considered in detail. The present paper generalizes much of that work to functions of many variables. In treating the case of functions of two variables whose Fourier transforms vanish outside a circle in the two-dimensional frequency plane, we are led to consider the integral equation $\gamma \varphi(x) = \int_{0}^{1} J_{N}(cxy) \sqrt{cxy} \varohi(y) dy. \qquad \eqno{\hbox{(i)}}$ It is shown that the solutions are also the bounded eigenfunctions of the differential equation $(1-x^{2}){d^{2}\varphi \over dx^{2}} - 2x {d \varphhi \over dx} +\left(x-c^{2}x^{2} + {{1 \over 4} - N^{2} \over x^{2}}\right) \varphi = 0. \qquad \eqno{\hbox{(ii)}}$ a generalization of the equation for the prolate spheroidal wave functions. The functions ϕ (called “generalized prolate spheroidal functions”) and the eigenvalues of both (i) and (ii) are studied in detail here, and both analytic and numerical results are presented. Other results include a general perturbation scheme for differential equations and the reduction to two dimensions of the case of functions of D > 2 variables restricted in frequency to the D sphere.
755 citations
"Phaseless Antenna Characterization ..." refers background in this paper
...they extend the usual properties of the PSWFs [17], [23]....
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...In the case of a circular aperture, when also the sinc sampling expansion of the PWS [27] is suboptimal [28], and are both circles, again if the whole visible region is of interest [23], [24]....
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